An in-host HIV-1 infection model incorporating quiescent and activated CD4⁺ T cells as well as CTL response

A mathematical model is proposed to capture the implication of quiescent and activated CD4⁺ T cells as well as the cytotoxic T lymphocyte (CTL) response on HIV-1 infection in an early stage. It underlies the different mechanisms behind the productive and latent infection, whereby virion-cell contact, cell-cell contact, immune response, slow-kinetic viral reverse transcription in quiescent cells, lytic death, pyroptosis, and virus survival play their significant role within. The existence, uniqueness, and global stability of both the virus-free and endemic equilibrium with respect to the magnitudes of the basic reproduction ratio are studied. Due to technical difficulties in revealing the close form of the endemic equilibrium, determining the whole picture of forward bifurcation around the virus-free states is accomplished with the aid of bifurcation theory. The sufficient condition for the forward bifurcation is satisfied by the choices of the parameter values, and simulations are presented to illustrate the analytical findings. In an effort to study which parameters can be attacked through the applications of RTIs, PIs, and vaccination toward foremost reduction of the basic reproduction ratio, a local sensitivity analysis is presented. Finally, a model version combining productive and latent infection, also treating disparate time scales from CD4⁺ T cells and CTLs as well as virions is studied. As long as any solution trajectory is initiated around the stable part of the critical manifold, it approaches and stays around the manifold and eventually lands in the manifold when the lifespans of CTLs and virions are comparably small. If the corresponding basic reproduction ratio is sufficiently large, then not only does the endemic equilibrium locate in the unstable part of the critical manifold, but all the solution trajectories (from the stable part) converge to the equilibrium due to global stability, indicating the existence of canards.